Munich Personal RePEc Archive

Stochastic discounting in repeated games: Awaiting the almost inevitable

Barlo, Mehmet and Urgun, Can (2011): Stochastic discounting in repeated games: Awaiting the almost inevitable.

This is the latest version of this item.

[img]
Preview
PDF
MPRA_paper_32544.pdf

Download (303kB) | Preview

Abstract

We study repeated games with pure strategies and stochastic discounting under perfect information, with the requirement that the stage game has at least one pure Nash action profile. Players discount future payoffs with a common, but stochastic, discount factor where associated stochastic discounting processes are required to satisfy Markov property, martingale property, having bounded increments, and possessing state spaces with rich ergodic subsets. We, additionally, demand that there are states resulting in discount factors arbitrarily close to 0, and that they are reachable with positive (yet, possibly arbitrarily small) probability in the long run. In this setting, we prove both the perfect Folk Theorem and our main result: The occurrence of any finite number of consecutive repetitions of the period Nash action profile, must almost surely happen within a finite time window no matter which subgame perfect equilibrium strategy is considered and no matter how high the initial discount factor is.

Available Versions of this Item

UB_LMU-Logo
MPRA is a RePEc service hosted by
the Munich University Library in Germany.